Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization
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Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and nonconvex cases. Most of them require a large number of samples in some or all iterations of the improved SGMs. In this paper, we propose a new SGM, named PStorm, for solving nonconvex nonsmooth stochastic problems. With a momentum-based variance reduction technique, PStorm can achieve a near-optimal complexity result Õ(ε^-3) to produce a stochastic ε-stationary solution, if a mean-squared smoothness condition holds. Different from existing near-optimal methods, PStorm requires only one or O(1) samples in every update. With this property, PStorm can be applied to online learning problems that favor real-time decisions based on one or O(1) new observations. In addition, for large-scale machine learning problems, PStorm can generalize better by small-batch training than other near-optimal methods that require large-batch training and the vanilla SGM, as we demonstrate on training a sparse fully-connected neural network.
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